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ASYMPTOTIC APPROXIMATION FOR THE SOLUTION TO THE ROBIN PROBLEM IN A THICK MULTI-LEVEL JUNCTION

Dipartimento di Matematica e Applicazioni,Università degli Studi di Napoli Federico II, Complesso Monte S. Angelo — Edificio "T", Via Cintia, 80126 Napoli, Italia

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T. DURANTE

Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell'Informazione e Matematica Industriale, Università di Cassino, via G. Di Biasio n.43, 03043 Cassino (FR), Italy

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T. A. MEL'NYK

Faculty of Mathematics & Mechanics, Taras Shevchenko National University of Kyiv, Volodymyrska str. 64, 01033 Kyiv, Ukraine

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https://doi.org/10.1142/S0218202505001011Cited by:31 (Source: Crossref)

Abstract

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ω_ε, which is the union of a domain Ω₀ and a large number 2N of thin rods with variable thickness of order . The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The Robin conditions are given on the lateral boundaries of the thin rods. Using the method of matched asymptotic expansions, we construct the asymptotic approximation for the solution as ε → 0 and prove the corresponding estimates in the Sobolev space H¹(Ω_ε).

Keywords:

AMSC: 35B27, 35B40, 35C20, 74K30

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